Vector field, source of a

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A point of the vector field with the property that the flow of the field through any sufficiently small closed surface enclosing it is independent of the surface and positive. The flow

where is the outward unit normal to and is the area element of , is called the power of the source. If is negative, one speaks of a sink. If the sources are continuously distributed over the domain considered, then the limit

is called the density (intensity) of the source at the point . It is equal to the divergence of at .


A combination of a source and a vortex in a hydrodynamical flow gives rise to a swirl flow.


[a1] J. Marsden, A. Weinstein, "Calculus" , 3 , Springer (1988)
[a2] H. Triebel, "Analysis and mathematical physics" , Reidel (1986) pp. Sect. 16
How to Cite This Entry:
Vector field, source of a. A.B. Ivanov (originator), Encyclopedia of Mathematics. URL:,_source_of_a&oldid=15332
This text originally appeared in Encyclopedia of Mathematics - ISBN 1402006098